That's the snapshot. But what's the story of how it's changed over time? Why is the participation rate declining? Let's investigate.

First, the very, very big picture. The prime-age participation rate (in GREEN below) has increased since the 1950s, where this graph begins on the left. Overall, Americans are more likely to be working than they were in the early 1970s. That's because more women between the age of 25 and 54 are working (seen in PINK), even though fewer men of that age are working than at any time in the last 60 years (in BLUE).

The big shifts of the last 20 years have been among the youngest and oldest adults. The group with the largest decline in participation has been teenage men. The group with the largest gains in participation have been 60-something women. Here's a look at the big movers between 1990 and 2010.

Why are young people, and especially young men, dropping out of the labor force? As Conor Sen explained for The Atlantic, there are good reasons (e.g.:more of them are going to college) and there are bad reasons (e.g.: more of them are hanging out at home playing video games, waiting for the job market to thaw).

Older people are working more because they can (it's not a factory-and-farm economy any more) and because they must (families don't save much on their own, so many hope to work longer into what used to be retirement). But don't be confused by rates and levels: Older people might be more likely to work than they used to be, but they're still unlikely to be working.

That sounds like an obvious point. But it's a big deal. It explains why an aging country will inevitably work less. Below is a picture of participation rates by age. Imagine a large generation, like the Boomers, moving through this picture, like an elephant through a snake. Their participation will naturally fall off. Each year after their mid-50s, the cohort will be less likely to work.

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Indeed, that's precisely what demographers have long predicted: The slow decline of the participation rate from this decade through the 2030s, as the Boomers moved into retirement. Those predictions are represented by the dotted lines below. The red line represents what's actually happened.

This very important picture tells us two things. First, the participation rate was expected to drop, with or without a recession. Second, the drop is happening much faster than we expected. The economy is behaving as though it's 2025 rather than 2013. What pushed the participation rate down prematurely?

The obvious answer is that the recession happened. The recession effect on participation rates is pretty clear when you zoom in on the data. The participation rate for both black men and white men over 20 years old has dropped 4 to 5 percent since the recession struck; for women, the drop has been about 2.5 percent.

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But the recession's effect is more complicated than you might think. According to a new paper by Kerwin Kofi Charles, Erik Hurst, and Matthew J. Notowidigdo, what we're really seeing is the decline of manufacturing, which is only being felt now because the band-aid provided by a temporary construction bubble was ripped clean off the labor market. Nearly 40 percent of the increase in non-working Americans between 2000 and 2011 "can be attributed to manufacturing decline," they wrote. The housing boom shifted some of these jobs to construction. But after the bust, the crutch was gone -- and so were the workers.

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It's about time for an upshot. So, where did all the workers go? Four answers, in order of importance.

(1) They retired. The country is getting older, and older countries have a smaller share of workers.

(2) They went to school. More young people are going to college, and young people in college are less likely to look for work.

(3) They just stayed home -- they stopped looking for work and decided instead to raise their kids; they sat on the couch waiting for the market to thaw; they filed for disability insurance. The recession discouraged them from seeking a job.

(4) And the factories closed. Behind all of these stories lurks the long decline of manufacturing, which has very little to do with the Great Recession, or college attendance, or demographics, but nonetheless explains a significant portion of falling participation rates among prime-age workers.

So there you have it, the answer to the 37 percent mystery in five words: Retirement, college, recession, and manufacturing.